We will refer to the two-sided bar construction as the bar construction, for short.
We can use the bar construction to model the homotopy colimit in \({{K}}_\infty \)  as follows [1]}:
\(\underset{{I}}{{\mathrm {hocolim}}}^{{{K}}_\infty } (E)\simeq B^{{{K}}_\infty }(*, {I}, Q^{{{K}}_\infty } \circ E)\,,\) 
